The strain amplitude dependent internal friction at room temperature and the transition temperatures of CuAlMn-shape memory alloys with Al contents from 8.9 wt.% to 12.7 wt.% and Mn contents from 4.7 wt.% to 9.3 wt.% were investigated. The investigated strain range was 10-6 - 10-3. Rods of various compositions were die cast and machined to single clamped damping bars. Their transition temperatures and amplitude dependent damping was determined in as cast and homogenized state. The damping in the investigated shape memory alloys was found to be generally much higher than in metals without martensitic transition. In as cast state some alloys exceeded the damping of a Sonoston type alloy measured in comparison for strains higher than 3 x 10-5. The influence of grain size on damping was investigated by additional sand casting and the use of Boron for grain refinement. It was found that only the material with the biggest grains had a noticeable higher damping over the whole measured strain range. Homogenization heat treatment can still extremely increase the damping of CuAlMn alloys. After homogenization this extremely high damping decreases slowly to medium values in the order of as cast alloys.